Polynomial optimization has a wide range of practical applications in fields
such as optimal control, energy and water networks, facility location, management science, and finance. It also
generalizes relevant optimization problems thoroughly studied in the literature, such as mixed-binary linear
optimization, quadratic optimization, and complementarity problems. As finding globally optimal solutions is an
extremely challenging task, the development of efficient techniques for solving polynomial optimization problems is
of particular relevance. In this thesis we provide a detailed study of different techniques to solve this kind of
problems and we introduce some nobel approaches in this field, including the use of statistical learning techniques.
Furthermore, we also present a practical application of polynomial optimization to finance and more specifically,
portfolio design
